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We show that every retral continuum with the fixed point property is locally connected. It follows that an indecomposable continuum with the fixed point property is not a retract of a topological group.

Rigid extensions of $ℓ$ -groups of continuous functions

Michelle L. Knox, Warren Wm. McGovern (2008)

Czechoslovak Mathematical Journal

Let $C (X, ℤ)$ , $C (X, ℚ)$ and $C (X)$ denote the $ℓ$ -groups of integer-valued, rational-valued and real-valued continuous functions on a topological space $X$ , respectively. Characterizations are given for the extensions $C (X, ℤ) \leq C (X, ℚ) \leq C (X)$ to be rigid, major, and dense.

Rigid P-spaces

Kenneth Kunen (1989)

Fundamenta Mathematicae

Ring epimorphisms and $C (X)$ .

Barr, Michael, Burgess, W. D., Raphael, R. (2003)

Theory and Applications of Categories [electronic only]

Rings of continuous functions vanishing at infinity

Ali Rezaei Aliabad, F. Azarpanah, M. Namdari (2004)

Commentationes Mathematicae Universitatis Carolinae

We prove that a Hausdorff space $X$ is locally compact if and only if its topology coincides with the weak topology induced by $C_{\infty} (X)$ . It is shown that for a Hausdorff space $X$ , there exists a locally compact Hausdorff space $Y$ such that $C_{\infty} (X) ≅ C_{\infty} (Y)$ . It is also shown that for locally compact spaces $X$ and $Y$ , $C_{\infty} (X) ≅ C_{\infty} (Y)$ if and only if $X ≅ Y$ . Prime ideals in $C_{\infty} (X)$ are uniquely represented by a class of prime ideals in $C^{*} (X)$ . $\infty$ -compact spaces are introduced and it turns out that a locally compact space $X$ is $\infty$ -compact if and only if every...

Rings of Real-Valued Continuous Functions. II.

Mikhail Y. Antonovskij (1981)

Mathematische Zeitschrift

Rings Of Real-Valued Functions And The Finite Subcovering Property.

Alexander Abian, Sergio Salbany (1979)

Revista colombiana de matematicas

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